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We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…
In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…
We calculate the decay rate for a state prepared in a thermal density matrix centered on a metastable ground state. We find a rate that is intrinsically time {\it dependent}, as opposed to the {\it constant} rates of previous works. The…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…
This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust…
A general decentralized computational framework for set-valued state estimation and prediction for the class of systems that accept a hybrid state machine representation is considered in this article. The decentralized scheme consists of a…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…
In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the…
We analyze a space-time hybridizable discontinuous Galerkin method to solve the time-dependent advection-diffusion equation on deforming domains. We prove stability of the discretization in the advection-dominated regime by using weighted…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
In this paper, we investigate stability in distribution of neutral stochastic functional differential equations with infinite delay (NSFDEwID) at the state space \begin{equation*} C_{r}=\{{\varphi\in…
We consider linear iterative schemes for the time-discrete equations stemming from a class of nonlinear, doubly-degenerate parabolic equations. More precisely, the diffusion is nonlinear and may vanish or become multivalued for certain…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a…
This paper considers the problem of multi-agent distributed optimization. In this problem, there are multiple agents in the system, and each agent only knows its local cost function. The objective for the agents is to collectively compute a…